A fundamental problem in the field of signal processing is the removal of unwanted "noise" signals from combination with a desired, or base, signal. The unwanted noise signals often arise from one or more sources and become mixed with the desired signal, due to one or more different reasons, to define a composite signal. Often, the desired signal has a periodic waveform with a particular characteristic frequency (i.e., such desired signals being referred to herein as "periodic signals"), while the unwanted "noise" signals have aperiodic waveforms (i.e., such unwanted "noise" signals having aperiodic waveforms being referred to herein as "aperiodic signals"), periodic waveforms with characteristic frequencies different than the characteristic frequency of the desired signal, or waveforms which are out of phase with the desired signal. The presence of such noise signals with periodic signals that are communicated from one site to another frequently requires the use of increased transmitter power or larger receiving antennas to ensure accurate communication of the periodic signals.
Over the years, engineers working in the field of signal processing have grappled with the problem of removing unwanted noise signals from a composite signal in order to increase the signal-to-noise ratio ("SNR") of a composite signal and have developed a number of techniques and systems for removing the unwanted noise signals. One such technique involves the use of systems which employ frequency filters that receive an incoming signal comprised of a desired signal and one or more noise signals (i.e., a composite input signal) and produce an outgoing signal which includes the desired signal and no noise signals or a reduced number of noise signals. In such cases, the desired signal has a characteristic frequency, while the unwanted noise signals have characteristic frequencies different than that of the desired signal. Frequency filters take advantage of the difference in frequencies by enabling passage of signals having frequencies above or below a threshold filtering frequency and by blocking passage of signals having frequencies conversely above or below the threshold filtering frequency.
While frequency filters function quite well in practice, they suffer from several disadvantages. First, in many cases, at least two stages of frequency filters must be employed to remove unwanted noise signals from a composite signal, thereby increasing the cost of a device which employs the frequency filters. The necessity of employing two stages of frequency filters arises because a first stage frequency filter is necessary to remove unwanted noise signals having frequencies below a threshold filtering frequency (i.e., the frequency of the desired signal) and a second stage frequency filter is necessary to remove unwanted noise signals having frequencies above a threshold filtering frequency. Second, in some cases, the desired signal and a noise signal have substantially the same characteristic frequency and, as a result, frequency filters cannot block passage of the noise signal without also blocking passage of the desired signal.
Another fundamental problem in the field of signal processing is the effects of time quantization that arise when digital sampling techniques are employed to minimize the transmission bandwidth required for communication of an analog signal. Such digital sampling techniques typically enable very accurate reproduction of the amplitude of the analog signal, but less than accurate reproduction of the waveform of the analog signal unless the analog signal is sampled many times per cycle. Digital transmission of the analog signal is, therefore, subject to a trade-off between the number of samples taken per cycle of the analog signal and the accuracy of the reproduction of the signal's waveform. The limit of sample economy is expressed by Nyquist's Theorem which states that a waveform cannot be appropriately represented and reproduced unless the waveform is sampled at least twice per cycle.
While in many applications the effects of time quantization are of little importance, the effects are very important in signal processing systems which reproduce human speech and music. Such systems must accurately reproduce speech and music because the human ear requires high-quality reproduction of analog signal waveforms. Unfortunately, because the accuracy of reproduction is limited by Nyquist's Theorem, a relatively large number of samples is required to produce the necessary accuracy.
Therefore, there is a need in the industry for a phase coherence filter which improves the signal-to-noise ratio of a composite signal, which enables accurate reproduction of a waveform using a lower sampling rate than that called for by Nyquist's Theorem, and which addresses these and other related, and unrelated, problems.